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Trignometry
(Trignometric Ratios And Identities)
Part-1
Math: Trignometry Chapter
The word trignometry is devided from 2 greek words
(1) Trigonon and (2) Meetron
Trignon means triangle and metron means measure So, is science of measuning angle .A very
interesting branch, it is used in almost all other branches of mathematic whether it be
coordinatc goemetry or it be calculus.
For a given angle in a right angle these ate six fossible ratios of 2 sides and hence there are 6
trignometric functions. These are extremely useful in simplefying many cliculations in
mathematics. So lets stady these in more details.
Trignometric functions:
Let O be centre if circle of radius r . Let a may po form an angle
pm.
So, in
sin
=
at centre of circle. Drop a
OPM we obserre.
, cos =
ton =
;
Further more about these 6 trignometric ratios is covered in this table.
Illustration 1.
Find the solr of the equation eln cos x = 2 ?
eln cos x = cos x lne = cos x
cos x = 2
Now the range of cos x is - 1 to 1 .
So, the equation has no solution .
Trignometric function of allied angles:
If
is any angle then -
,
Remork: (1) If we have allied angle
etc are called allied angles of
where n is any integer then ratio remains the
some and sign ( +ve and -ve) is given according to the quadrant in which
(assuming
lies
st
I Quadrant).
(2) If we have allied angle
where P is an odd integer then ratio changes i.e 'sine'
changs to 'cosine' ; 'cosine' changes t 'sine'; tangent and 'cosecant' changes to 'secant'changes to
'cotangent', 'secant' changes t 'cosecant' and ' cosecant' changes to 'secant' The sign (+ve or -ve )
is given according t quadrant in which
lies(assumtg
IstQuadrant